SIGNAL ALIASING IN GAUSSIAN RANDOM FIELDS FOR EXPERIMENTS WITH QUALITATIVE FACTORS

• Published in: The Annals of statistics 2019-04, Vol.47 (2), p.909-935
• Main Authors: Chang, Ming-Chung, Cheng, Shao-Wei, Cheng, Ching-Shui
• Format: Article
• Language: English
• Subjects: Aliasing; Bayesian analysis; Covariance; Fault diagnosis; Fields (mathematics); Normal distribution; Signal processing
• ISSN: 0090-5364; 2168-8966
• DOI: 10.1214/18-AOS1682

Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the covariance function. The aliasing severity of the signals is determined by two key elements: (i) the aliasing pattern, which depends only on the chosen design, and (ii) the effect priority, which is related to the variances of the random effects and depends on the model parameters. We first apply this framework to study the signal-aliasing problem for regular fractional factorial designs. For general factorial designs including nonregular ones, we propose an aliasing severity index to quantify the severity of signal aliasing.We also observe that the aliasing severity index is highly correlated with the prediction variance.